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Coprime is an English word. Below you'll find 10+ example sentences showing how it's used in practice.

Rare word

Coprime in a sentence

Coprime meaning

  1. Having no positive integer factors in common, aside from 1.
  2. Having no positive integer factors, aside from 1, in common with one or more specified other positive integers.
  3. Whose greatest common divisor is a nonzero constant (i.e., polynomial of degree 0).

Using Coprime

  • The main meaning on this page is: Having no positive integer factors in common, aside from 1. | Having no positive integer factors, aside from 1, in common with one or more specified other positive integers. | Whose greatest common divisor is a nonzero constant (i.e., polynomial of degree 0).
  • In the example corpus, coprime often appears in combinations such as: are coprime, coprime if, pairwise coprime.

Context around Coprime

  • Average sentence length in these examples: 25.4 words
  • Position in the sentence: 4 start, 10 middle, 6 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

pairwise 5× setwise 1×

Often after:

pairs 2× finite 1× amicable 1×

Sentence patterns with Coprime

These short patterns come directly from the example sentences and show how the word is often embedded:

b are coprime if and 2× 1 are coprime 1× 1 are coprime to n 1× also setwise coprime but the 1× and are coprime 1× and n coprime and of 1× are pairwise coprime 1× are pairwise coprime if the 1×

Sentence openings and endings

Common sentence openings:

a set of 1× also a pair 1× case of two 1× equivalently n is 1× for a fixed 1× for this let 1×

Common sentence endings:

1 are coprime 1× and are coprime 1× any other rotor 1× any similar formula 1× are all different 1× are pairwise coprime 1×

Words around Coprime

Just before it in the word index:

copresident 2 copra 42 coppull 2 copps 4 coppola 200 coppock 9

Just after it in the word index:

coprocessor 28 coprocessors 9 coprodeum 4 coproduced 3 coproduct 5 coproduction 5

Similar in corpus frequency:

abattoirs 30 abike 30 ablative 30 absorber 30 accel 30 accelerometer 30

Corpus analysis for Coprime

  • In this selection, "coprime" usually appears in the middle of the sentence. The average example has 25.4 words, and this corpus slice is mostly made up of statements.
  • Around the word, pairwise, setwise, pairs, finite and amicable stand out and add context to how "coprime" is used.
  • Recognizable usage signals include b are coprime if and and 1 are coprime. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "coprime" sits close to words such as abattoirs, abike and ablative, which helps place it inside the broader word index.

Example types with coprime

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

It is possible for an infinite set of integers to be pairwise coprime. (13 words)

Generating all coprime pairs The order of generation of coprime pairs by this algorithm. (14 words)

Case of two moduli We want to solve the system : where and are coprime. (14 words)

Longer example sentences

A set of integers can also be called coprime if its elements share no common positive factor except 1. A set of integers is said to be pairwise coprime if a and b are coprime for every pair (a, b) of different integers in it. (45 words)

For a fixed value of n it is multiplicative in q: :If q and r are coprime, Many of the functions mentioned in this article have expansions as series involving these sums; see the article Ramanujan's sum for examples. (40 words)

Some rotor machines were designed with a different number of pins on each rotor, with the number of pins on any one rotor either prime, or coprime to the number of pins on any other rotor. (36 words)

Example sentences (20)

A set of integers can also be called coprime if its elements share no common positive factor except 1. A set of integers is said to be pairwise coprime if a and b are coprime for every pair (a, b) of different integers in it.

Generating all coprime pairs The order of generation of coprime pairs by this algorithm.

Pairwise coprimality is a stronger condition than setwise coprimality; every pairwise coprime finite set is also setwise coprime, but the reverse is not true.

Two natural numbers a and b are coprime if and only if the numbers 2 a 1 and 2 b 1 are coprime.

Also, a pair of coprime amicable numbers cannot be generated by Thabit's formula (above), nor by any similar formula.

Case of two moduli We want to solve the system : where and are coprime.

Equivalently, n is prime if and only if all integers m satisfying 2 ≤ m ≤ n − 1 are coprime to n, i.e. their only common divisor is one.

For a fixed value of n it is multiplicative in q: :If q and r are coprime, Many of the functions mentioned in this article have expansions as series involving these sums; see the article Ramanujan's sum for examples.

Advertentie

For this, let us consider k monic polynomials of degree one: : They are pairwise coprime if the are all different.

General case Let us consider a sequence of congruence equations : where the are pairwise coprime.

If a and b are coprime and a divides the product bc, then a divides c. This can be viewed as a generalization of Euclid's lemma.

If two numbers have no prime factors in common, their greatest common divisor is 1 (obtained here as an instance of the empty product ), in other words they are coprime.

In case a denominator and numerator remain that are too large to ensure they are coprime by inspection, a greatest common divisor computation is needed anyway to ensure the fraction is actually irreducible.

In this determination, it is convenient to use the characterization that a and b are coprime if and only if no prime number divides both of them (see Fundamental theorem of arithmetic ).

It is possible for an infinite set of integers to be pairwise coprime.

One may thus equate numerators with numerators and denominators with denominators, giving Euclid's formula : with m and n coprime and of opposite parities.

Probabilities Given two randomly chosen integers a and b, it is reasonable to ask how likely it is that a and b are coprime.

Some rotor machines were designed with a different number of pins on each rotor, with the number of pins on any one rotor either prime, or coprime to the number of pins on any other rotor.

The natural numbers m and n must be coprime, since any common factor could be factored out of m and n to make g greater.

Then solving : for and gives : As is fully reduced, m and n are coprime, and they cannot be both even.

Advertentie

Common combinations with coprime

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "coprime" in a sentence?
An example: "A set of integers can also be called coprime if its elements share no common positive factor except 1. A set of integers is said to be pairwise coprime if a and b are coprime for every pair (a, b) of different integers in it." This page contains 10+ example sentences with the word "coprime" from authentic English texts.
What does "coprime" mean?
Coprime means: Having no positive integer factors in common, aside from 1.
How many example sentences with "coprime" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "coprime", drawn from a database of millions of English sentences.